England.

# Learning and doing algebra

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This module examines the nature of algebra and how children learn. It develops your awareness of choosing and using symbols and your ability to express general mathematical statements. You’ll meet ideas about learning and teaching algebra, such as the progressions from number to algebra and the importance of communicating and interpreting relationships in words, diagrams and graphs. You’ll also learn ways to identify and analyse your own and others’ algebraic reasoning. This module is a step towards qualifying and developing as a secondary or primary mathematics teacher, teaching assistant, tutor or parent educator.

## What you will study

The module comprises eight units:

Unit 1: The nature of algebra
You’ll meet some definitions of school algebra and algebraic thinking. You’ll tackle problems that approach algebra as a way of exploring and expressing generality. And read about moving between well-chosen examples and generalisations and appreciating the role of freedoms and constraints. Additionally, you’ll develop algebraic expressions for simple numerical problems and encounter ideas from research and classroom practice about learning to interpret and treat algebraic symbols.

Unit 2: Representing structural relationships
You’ll tackle problems involving making your algebraic conjectures and convincing yourself when these are true. Taking an approach that algebra is a way of noticing underlying structure, you’ll meet a range of early-algebraic representations used in classrooms, such as bar models and Cuisenaire rods. You’ll read about choosing algebraic representations and work on problems with a learner.

Unit 3: The power of symbolising
This unit focuses on the power of using algebra symbols and the difficulties people experience. You’ll reflect on the choices we make when symbolising and how symbols help create convincing proofs. Additionally, you’ll meet the module idea ‘Manipulate, Get a sense of, Articulate’ that connects learning progression with choice of representations.

Unit 4: Equivalence and the equals sign
You’ll read and tackle problems that help you to notice different ways in which numeric and algebraic expressions can be equivalent, including how learners use the equals sign. You’ll meet two new module ideas: ‘Doing and undoing’ underpins some widely used methods of solving linear equations; ‘Productive lingering’ describes how teachers take time over small steps of algebraic reasoning. You’ll also undertake a project where you adapt a given task and work on it with your learner.

Unit 5: Invariance and change
You’ll focus on algebraic thinking as noticing change and, amidst this change, expressing properties or relationships stay the same. You’ll tackle problems that require you to organise and represent change in one or more variables, particularly sequences problems. Additionally, you’ll create a presentation that identifies invariance and change in your algebraic reasoning.

Unit 6: Covariant relationships
This unit focuses on covariation: how two or more variables change in relation to one another. You’ll tackle problems involving algebraic expressions and graphs. You’ll also learn to use Cornerstone Maths and Geogebra, two digital environments designed for education, to depict covariant relationships and reflect on the affordances of different representations.

Unit 7: Exploring functions and graphs
You’ll focus on functions, including the properties and contexts that give rise to linear, quadratic and exponential functions. Then, having now met all the module ideas, you’ll choose appropriate ones to identify algebraic thinking in your own mathematics and that of your learner. This forms the basis of your end-of-module assessment.

Unit 8: Progressing to geometry
This final unit makes connections between algebra and geometry, supporting progression to Learning and doing geometry (ME321).

You can find the full content list on the Open mathematics and statistics website.

### You will learn

You’ll learn to:

• apply ideas from the field of mathematics education for analysing algebraic thinking and learning, specialising in the algebraic content and processes relevant to 11–16-year-olds
• apply a range of approaches to algebraic problems in your own mathematics and in interpreting learners’ algebraic activity
• formulate approaches to teaching
• communicate algebraic thinking, including adapting problems to suit learners
• formulate a personal perspective on issues covered in the module and reflect on developments in your thinking
• use graphing software to support the learning of algebra.

## Entry requirements

There is no formal pre-requisite study, but we recommend that you study Mathematical thinking in schools (ME620) before or alongside this module.

The ability to write reports in good English is needed for the assignments. You can find support developing academic English in our Help Centre.

## Preparatory work

The free course Teaching mathematics is good preparation for this module, particularly Weeks 4 and 5.

## What's included

• a week-by-week study planner
• course-specific module materials
• audio and video content, filmed in schools
• independent study readings from the OU Library
• free educational software
• assignment details and submission section
• online tutorial access.

We’ll also provide you with three printed algebra task booklets, each covering 2–3 units of study.

### Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.

### Assessment

The assessment details for this module can be found in the facts box.

## If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying ME322 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

## Future availability

Learning and doing algebra (ME322) starts once a year – in October.

We expect it to start for the last time in October 2029.

### Course work includes:

3 Tutor-marked assignments (TMAs)
End-of-module assessment

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